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We develop efficient and effective strategies for the update of Katz centralities after node and edge removal in simple graphs. We provide explicit formulas for the ``loss of walks" a network suffers when nodes/edges are removed, and use these to inf
Externí odkaz:
http://arxiv.org/abs/2411.19560
We extend the notion of nonbacktracking walks from unweighted graphs to graphs whose edges have a nonnegative weight. Here the weight associated with a walk is taken to be the product over the weights along the individual edges. We give two ways to c
Externí odkaz:
http://arxiv.org/abs/2202.02888
We study walk-based centrality measures for time-ordered network sequences. For the case of standard dynamic walk-counting, we show how to derive and compute centrality measures induced by analytic functions. We also prove that dynamic Katz centralit
Externí odkaz:
http://arxiv.org/abs/2110.10526
Autor:
Arrigo, Francesca, Durastante, Fabio
Publikováno v:
SIAM J. Matrix Anal. Appl., 42(4), 2021
We describe a complete theory for walk-based centrality indices in complex networks defined in terms of Mittag-Leffler functions. This overarching theory includes as special cases well-known centrality measures like subgraph centrality and Katz centr
Externí odkaz:
http://arxiv.org/abs/2103.12559
We develop a complete theory for the combinatorics of walk-counting on a directed graph in the case where each backtracking step is downweighted by a given factor. By deriving expressions for the associated generating functions, we also obtain linear
Externí odkaz:
http://arxiv.org/abs/2012.02999
We propose and analyse a general tensor-based framework for incorporating second order features into network measures. This approach allows us to combine traditional pairwise links with information that records whether triples of nodes are involved i
Externí odkaz:
http://arxiv.org/abs/1910.12711
Autor:
Arrigo, Francesca, Tudisco, Francesco
We introduce a ranking model for temporal multi-dimensional weighted and directed networks based on the Perron eigenvector of a multi-homogeneous order-preserving map. The model extends to the temporal multilayer setting the HITS algorithm and define
Externí odkaz:
http://arxiv.org/abs/1809.08004
Publikováno v:
In Linear Algebra and Its Applications 15 December 2022 655:159-185
Eigenvector-based centrality measures are among the most popular centrality measures in network science. The underlying idea is intuitive and the mathematical description is extremely simple in the framework of standard, mono-layer networks. Moreover
Externí odkaz:
http://arxiv.org/abs/1711.08448